The drawing shows two long, thin wires that carry currents in the positive z direction. Both wires are parallel to the z axis. The 50-A wire is in the x-z plane and is 5 m from the z axis. The 40-A wire is in the y-z plane and is 4 m from the z axis. What is the magnitude of the magnetic field at the origin?

The magnitude of the magnetic field at the origin is .

Explanation:

Given :

50-A wire is in the x-z plane and is 5 m from the z axis.

Also , 40-A wire is in the y-z plane and is 4 m from the z axis.

Now , since both the wire are perpendicular to each other .

Therefore , magnetic field are also perpendicular to each other .

Magnetic field at origin due to wire 1 is :

Magnetic field at origin due to wire 2 is :

Now , therefore net magnetic field is :

Putting value of

We get ,

Therefore, the magnitude of the magnetic field at the origin is .